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Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficients

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  • We prove heat kernel bounds for the operator $(1+|x|^\alpha)\Delta$ in $\mathbb{R}^N$, through Nash inequalities and weighted Hardy inequalities.
    Mathematics Subject Classification: 47D07, 35B50, 35J25, 35J70.


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  • [1]

    A. Bazan and W. NevesThe Caffarelli-Kohn-Niremberg's inequality for arbitrary norms, preprint.


    A. Bazan and W. NevesThe Hardy and Caffarelli-Kohn-Niremberg inequalities revised, preprint, arXiv:1007.2005v1.


    D. Bakry, F. Bolley, I. Gentil and P. MaheuxWeighted Nash inequalities, preprint, arXiv:1004.3456.


    E. B. Davies, "One-Parameter Semigroups," London Mathematical Society Monographs, 15, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980.


    E. B. Davies, "Heat Kernels and Spectral Theory," Cambridge Tracts in Mathematics, 92, Cambridge University Press, Cambridge, 1989.


    K.-J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolutions Equations," Graduate Texts in Mathematics, 194, Springer-Verlag, New York, 2000.


    S. Fornaro and L. Lorenzi, Generation results for elliptic operators with unbounded diffusion coefficients in $L^p$- and $C_b$-spaces, Discrete and Continuous Dynamical Systems, 18 (2007), 747-772.


    G. Metafune, E. M. Ouhabaz and D. Pallara, Long time behavior of heat kernels of operators with unbounded drift terms, J. Math. Anal. Appl., 377 (2011), 170-179.doi: 10.1016/j.jmaa.2010.10.023.


    G. Metafune and C. SpinaElliptic operators with unbounded diffusion coefficients in $L^p$ spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear.


    G. Metafune and C. Spina, Kernel estimates for a class of Schrödinger semigroups, Journal of Evolution Equations, 7 (2007), 719-742.doi: 10.1007/s00028-007-0338-3.


    G. Metafune, D. Pallara and M. Wacker, Feller semigroups on $\R^N$, Semigroup Forum, 65 (2002), 159-205.doi: 10.1007/s002330010129.


    B. Muckenhoupt, Hardy's inequalities with weights, Studia Math., 44 (1972), 31-38.


    B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., 192 (1974), 261-274.doi: 10.1090/S0002-9947-1974-0340523-6.


    E. M. Ouhabaz, "Analysis of Heat Equations on Domains," London Mathematical Society Monographs Series, 31, Princeton University Press, Princeton, NJ, 2005.


    F.-Y. Wang, Functional inequalities and spectrum estimates: The infinite measure case, J. Funct. Anal., 194 (2002), 288-310.doi: 10.1006/jfan.2002.3968.

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